Question

I was given this problem:

PART A:

Consider the following model of wage determination:

wage= 0+1educ+2exper+3married+ε

where:    wage = hourly earnings in dollars

    educ = years of education

    exper = years of experience

    married = dummy equal to 1 if married, 0 otherwise

Using data from the file ps2.dta, which contains wage data for a number of workers from across the United States, estimate the model shown above by OLS using the regress command in Stata. As always, be sure to include your Stata output (show the regression command used and the complete regression output).

Why are we unable to determine which of the included variables is the most important determinant of wages by simply looking at the size (and perhaps significance) of the estimated coefficients (even if we were confident that these estimates reflected unbiased causal impacts)?

My answer to PART A:

. regress wage educ exper married

     Source |       SS df       MS Number of obs  = 526

-------------+----------------------------------   F(3, 522) = 54.97

      Model |  1719.00074         3 573.000246 Prob > F        = 0.0000

   Residual |  5441.41355     522 10.4241639 R-squared       = 0.2401

-------------+----------------------------------   Adj R-squared = 0.2357

      Total |  7160.41429       525 13.6388844 Root MSE        = 3.2286

------------------------------------------------------------------------------

       wage |    Coef. Std. Err.      t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

       educ | .6128507   .0542332 11.30 0.000     .5063084 .7193929

      exper |   .0568845 .0116387     4.89 0.000 .0340201     .079749

    married |   .9894464 .309198     3.20 0.001 .3820212    1.596872

      _cons |  -3.372934   .7599027 -4.44   0.000 -4.865777 -1.880091

We are unable to determine which of the independent variables is the strongest predictor of wage because the predictors use different units of measurement.

Is this answer correct?

PART B:

Estimate the model again in Stata, but now include the “beta” option and explain how the additional information provided helps to provide insight into this issue discussed in part (c). As part of your answer, provide a clear interpretation of the new Stata output corresponding to the educ variable.  

My answer to PART B:

The “, beta” command, shows us the standardized coefficients and enables us to make a comparison of the independent variables’ relationship to the dependent variable; the higher the absolute value of the beta coefficient for each the independent variable, the stronger predictor it is of the dependent variable. The beta coefficient shows how one unit change in the independent variable’s standard deviation corresponds to a change in the standard deviation of the dependent variable. From the STATA output, are able to see that educ has the highest beta coefficient, meaning that education is the strongest predictor of wage. Whether or not someone is married is the weakest predictor of wage.

regress wage educ exper married, beta

     Source |       SS df       MS Number of obs  = 526

-------------+----------------------------------   F(3, 522) = 54.97

      Model |  1719.00074         3 573.000246 Prob > F        = 0.0000

   Residual |  5441.41355     522 10.4241639 R-squared       = 0.2401

-------------+----------------------------------   Adj R-squared = 0.2357

      Total |  7160.41429       525 13.6388844 Root MSE        = 3.2286

------------------------------------------------------------------------------

       wage |    Coef. Std. Err.      t P>|t|        Beta

-------------+----------------------------------------------------------------

       educ | .6128507   .0542332 11.30 0.000                 .4595065

      exper |   .0568845 .0116387     4.89 0.000     .2090517

    married |   .9894464 .309198     3.20 0.001     .1308998

      _cons |  -3.372934   .7599027 -4.44   0.000         .

Is my answer correct?

Answer 1

The answer is absolutely correct and needs no further explanations

wage |    Coef. Std. Err.      t P>|t|        Beta

-------------+----------------------------------------------------------------

       educ | .6128507   .0542332 11.30 0.000                 .4595065

      exper |   .0568845 .0116387     4.89 0.000     .2090517

    married |   .9894464 .309198     3.20 0.001     .1308998

      _cons | -3.372934   .7599027 -4.44   0.000

Just one more point , you must also look at the p values of the variables to ensure that the independent variable under question is statistically signficant for the model or not. if the p value is less than 0.01 (or assumed alpha ) then the variable is statistically signficant. Else the variable is not signficant for the model